Theoretical Golden Rule treatment of the dynamics of triplet and singlet excited-state intramolecular proton transfer (ESIPT) in 2-(2'-hydroxyphenyl)benzoxazole (HBO) and its derivative 2-(2'-hydroxy-4'-methylphenyl)-benzoxazole (MHBO) is presented. These compounds express typical and very similar non-Arrhenius temperature behavior of the rate of triplet keto-enol equilibration theta1 = k(K-E) + k(E-K) despite the experimental evidence of different reaction regimes and keto-enol energy gaps. In the method applied, all modes of the transferred atom (stretching, bending, and twisting) are taken into account, including an effective intramolecular promoting mode coupled to the H-motion, which is mainly responsible for the temperature dependence of the rate constant. Input data for the dynamic calculations is the standard output of the AM1 (structural and force field) results for both tautomers; the electronic coupling integral J is an adjustable parameter. The calculated rate theta1 is only slightly sensitive to the two experimentally suggested arrangements of the enol and keto triplet states (DELTAE = E(K) - E(E) = 0 and 9.9 kJ/mol for HBO and MHBO, respectively), as experimentally observed, and is in good agreement with the experimental results for both isotopes. The study of the singlet ESIPT in these compounds suggests that the primary reason for the rapidity of the process, as well as for the distinctions between the triplet and singlet transfer, is in electronic factors, mainly the electronic coupling.